Yixin He

collaborators

13 papers

math.CV2026

A counterexample to Nevanlinna's century-old half-plane problem

Yixin He, Teng Zhang

Let $H = {z \in C : Im z > 0}$ , and let $N (H)$ denote the Nevanlinna class in $H$ , consisting of meromorphic functions representable as…

math.OA2026

The solution to Kadison's problem on orthonormal bases of unitaries for type $II_{1}$ factors

Yixin He, Quanyu Tang, Zongben Xu +1

In 1967, Kadison asked whether every type $II_{1}$ factor admits an orthonormal basis, with respect to its trace, consisting of unitaries. We resolve this problem in full ge…

math.SP2026

Counterexamples to a higher-index Dirichlet eigenvalue-ratio conjecture

Yixin He, Quanyu Tang, Haiqi Zhang

Let $λ_{k} (Ω)$ denote the $k$ th Dirichlet Laplacian eigenvalue of a bounded planar domain $Ω$ , with eigenvalues counted with multiplicity. We disprove a conjectured higher-index exte…

math.CV2026

Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation

Pengcheng Fang, Yixin He

We settle two endpoint problems for Beurling--Carleson support conditions. For $0 < s < \frac{1}{2}$ and $θ = \frac{1 - 2 s}{1 - s}$ , we construct a nonatomic singular probability measure $μ$ , su…

math.FA2026

Variable-Radius Disk Transforms and an Area-Integral Problem of Zalcman

Qiteng Guo, Yixin He

For $0 < α \leq 1$ , define $(T_{α} f) (z) := \int_{B (z, α (1 - ∣ z ∣))} f (ζ) d A (ζ)$ for $z \in D$ , where $d A$ is planar Lebesgue measure. We prove that $T_{α}$ is injective…

math.SP2026

A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues

Yixin He, Yanyang Li, Quanyu Tang

We prove the Ashbaugh--Benguria conjecture for bounded domains with Lipschitz boundary in $R^{m}$ . More precisely, among all bounded Lipschitz domains of fixed volume, the ba…

math.OA2026

The separable case of Kadison's problem on orthonormal bases of unitaries for type $II_{1}$ factors

Yixin He, Quanyu Tang, Teng Zhang

In 1967, Kadison asked ``does every type $II_{1}$ factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov the…

math.CV2026

Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class

Yixin He, Quanyu Tang, Teng Zhang

We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.

math.CV2026

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

Yixin He, Quanyu Tang, Teng Zhang

We construct an entire function $F (z, a, b) \in O (C^{3})$ such that the family ${F (\cdot, a, b) : a, b \in C}$ of entire functions of $z$ is normal on…

math.CO2026

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

Yixin He, Quanyu Tang

Fix an integer $r \geq 2$ . For each $n$ we consider families $F \subseteq 2^{[n]}$ that form an antichain and have the property that, for every $t$ , if there exists $A\in\math…

math.CV2026

On Fuchs's additive intersection problem for the hyperbolic metric

Yixin He, Quanyu Tang

For hyperbolic domains $D_{1}, D_{2} \subset {z \in C : ∣ z ∣ < R}$ and $z \in D_{1} \cap D_{2}$ , we consider the ratio $\frac{λ _{D_{1} \cap D_{2}} ( z )}{λ _{D_{1}} ( z ) + λ _{D_{2}} ( z )} .$ We solve a pr…

math.CV2026

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

Yixin He, Quanyu Tang

Let $f (z) = \sum_{n \geq 0} a_{n} z^{n}$ be a transcendental entire function and write $M (r, f) := max_{∣ z ∣ = r} ∣ f (z) ∣$ and $μ (r, f) := max_{n \geq 0} ∣ a_{n} ∣ r^{n}$ . A problem of Erdős asks for the valu…

math.GM2024

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$

Keyu Chen, Wei He, Yixin He +7

Recently Shekhar Suman [arXiv: 2407.07121v6 [math.GM] 3 Aug 2024] made an attempt to prove the irrationality of $ζ (5)$ . But unfortunately the proof is not correct. In this note, we…

A counterexample to Nevanlinna's century-old half-plane problem

The solution to Kadison's problem on orthonormal bases of unitaries for type II1​ factors

Counterexamples to a higher-index Dirichlet eigenvalue-ratio conjecture

Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation

Variable-Radius Disk Transforms and an Area-Integral Problem of Zalcman

A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues

The separable case of Kadison's problem on orthonormal bases of unitaries for type II1​ factors

Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

An Erdős--Trotter problem on antichains with multiplicity r on each occurring level

On Fuchs's additive intersection problem for the hyperbolic metric

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

A Note on a Recent Attempt to Prove the Irrationality of ζ(5)

The solution to Kadison's problem on orthonormal bases of unitaries for type $II_{1}$ factors

The separable case of Kadison's problem on orthonormal bases of unitaries for type $II_{1}$ factors

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$